Panel Data Analysis

Definition

A panel data set is one that follows a given sample of units over time. Thus, panel data analysis refers to econometric tools that deal with the estimation of relationships that combine time series and cross-sectional data.

Denote by y_it an observation of the dependent variable for unit i at time t, and x_it the set of K independent variables observed for unit i at time t. Consider a linear regression model:

$$ {y}_{it}={\alpha}_{it}+{\beta}_{it}^{\prime }{x}_{it}+{u}_{it},i=1,\dots, N,t=1,\dots T, $$

(1)

where the error term u_it is independently and identically distributed over i and t, and α_it and ${\beta}_{it}^{\prime }$ are (1 × 1) and (K × 1) vectors of parameters to be estimated. This model cannot be estimated because the degrees of freedom, NT, is less than the number of parameters to be estimated, NT(K+ 1). Therefore, structure needs to be imposed. Assuming constant parameters over time, the basic initial test is the covariance test for homogeneity across units,...